Data from: The relative efficiency of modular and non-modular networks of different size

Most biological networks are modular but previous work with small model networks has indicated that modularity does not necessarily lead to increased functional efficiency. Most biological networks are large, however, and here we examine the relative functional efficiency of modular and non-modular neural networks at a range of sizes. We conduct a detailed analysis of efficiency in networks of two size classes: ‘small’ and ‘large’, and a less detailed analysis across a range of network sizes. The former analysis reveals that while the modular network is less efficient than one of the two non-modular networks considered when networks are small, it is usually equally or more efficient than both non-modular networks when networks are large. The latter analysis shows that in networks of small to intermediate size, modular networks are much more efficient that non-modular networks of the same (low) connective density. If connective density must be kept low to reduce energy needs for example, this could promote modularity. We have shown how relative functionality/performance scales with network size, but the precise nature of evolutionary relationship between network size and prevalence of modularity will depend on the costs of connectivity.绝大多数生物网络均具备模块化（modularity）特征，但此前基于小型模型网络开展的研究表明，模块化未必能提升功能效率。然而，绝大多数生物网络的规模均较为庞大，本研究针对不同尺度下模块化与非模块化神经网络的相对功能效率展开了系统分析。我们针对“小型”与“大型”两类规模等级的网络开展了精细化效率分析，并针对全尺度网络规模开展了概览性分析。前述精细化分析结果显示：当网络规模较小时，模块化网络的效率低于本次研究所考察的两类非模块化网络中的其中一种；但当网络规模扩大至大型时，模块化网络的效率通常与两类非模块化网络持平，甚至更高。而后开展的概览性分析则表明：在小型至中型规模的网络中，模块化网络的效率远高于具有相同（低）连接密度（connective density）的非模块化网络。例如，若需通过降低连接密度以减少能量消耗，该条件或将推动模块化特征的演化。本研究阐明了相对功能/性能随网络规模的变化规律，但网络规模与模块化普及程度之间的确切演化关系，将取决于连接成本的高低。